Maths PD at Kohia 14/3/18

These are my notes from the maths PD session I attended at Kohia on 14/3/18.
The presenter was Lucie Cheeseman.

Give one - get one strategy. Activating prior knowledge.

What does it mean to be numerate?

To be able to use maths in everyday life.

To problem solve.

To be mathematically literate.

Less emphasis these days on the right answer, more how did you get the answer?

Efficiency - we need to ensure, even with little kids, that they are solving problems efficiently.  
Unpack the word ‘efficient’ with little kids - we are looking for the quickest way, the way that
is going to take the smallest number of steps.  

Eg. Why would you count from 1 when you could count on from the bigger number.

Pictures and diagrams just as important as mathematical equations.

Knowledge and strategy are interlinked.

Ask questions, rather than give statements, so that children are doing the thinking,
not being dependent.  For example, show a number, say 11. “How could you show me this number?”
Children can choose which materials they use, which are most efficient for showing the number.

If you can answer in 4 seconds, that’s knowledge.  Longer than 4 seconds to process
you’re using a strategy.  

Kids learn more from each other than us.  This is a good reason for mixed-ability grouping.

To be meeting the standard after the first year at school they need to know the numbers
1-20 securely, to understand the place value not just read the numerals.

STAGES

Emergent

Stage 1 - 1:1 counting

Stage 2 - Counting from 1 on materials. A lot of kids will move straight from Stage 2 to Stage 4.  

Stage 3 - Counting from 1 by imaging (need to be working with relatively small numbers).  

Stage 4 - Advanced counting - AFTER 2 YEARS Counting on from the bigger number.

Encourage them to use their fingers to track their counting on. They need to be able to count
on or back from the bigger number using numbers 0-100.  

Stage 5 - Early Additive AFTER 3 YEARS

AT AFTER 4 YEARS.

They would solve a problem like 9+5 by splitting the 5, by knowing that 9+1=10, 10+4=14.

Stage 6 - Advanced Additive - Solving problems like 132-59.

Can show difference between two numbers with sets of counters.  Subtraction is not always
taking away or finding what’s left.

Set up examples where the algorithm is inefficient.  Like 1007-999 - it’s more efficient to
know that 1 makes 1000 and 7 makes 1007, 7+1=8, rather than using the algorithm.  

Book 1 of the Numeracy Project books has all the strategies and the expectations at the
different stages.  

Components of group teaching
Knowledge check - opportunity to activate prior knowledge- should be quick and pacy.  
Can have cards and get kids to read the number. “How many more do I need to make 10?”
/Quik pix - for example subitising images. You don’t necessarily want the kids to count.  
They can look at tens frame and get a sense of how many there are. Sketch when image is gone.
About 90 seconds to draw what they see. Site good for occasional maths chat - Maths Eyes.
When they’ve got the hang of that they can add numbers to their drawing to explain it.

Mathematical word problem - NZ Maths is good for word problems Eg. Pete the Cat -
good picture book series for mathematical ideas - link to word problems.  
Launch problem, hook children into problem. Example problem - additive strategies -
Pete the Cat and his brother Tom have 10 buttons to share between them.  
What are the different ways their buttons could be shared?
The teacher’s role during problem solving is to monitor, to ask deep questions,
but not to rescue children when they are struggling. “Spray and walk away.”  
Can physically take children to another table to see another group’s strategy.

Parallel problems - differentiation - same problems, change numbers.

Use cards with job descriptions for people in the group - can put on lanyards to start with.

Use of materials - children choose which materials will be the most efficient for solving
the problem.  
Can give them play opportunities first - eg. using toy cars as maths materials.

Thinking groups = collaboration

Modelling books/thinkboards - these should be a record of student learning.
 A thinkboard is a piece of paper divided into three sections:
“Clues,” “Mathematical Proof,” “Reflection - where are you in the learning pit?”  
Co-constructed WALT or LI - at end “Were we counting from 1 or were we counting
on from the bigger number?  Were we skip counting?” Then they leave the teacher with
the idea of what they were learning.

‘We’re a whanau,’ not ‘we’re a team.’  Supportive rather than competitive.

$2 shop microphone for child sharing thinking.  Teacher needs to make strategic
choices about which groups will share and the sequence in which they will share.  

Teaching Channel - good youtube channel for PD in different curriculum areas.

Take away: These are some ideas I'd like to use from this PD

Co-constructing WALT at end.

Try Quick pix for maths warmup.  

Use cars as a maths context.

‘Thinking thumb’ when you’re ready to share.

Can use ‘what’s the pattern?’ rather than ‘what’s the answer?’

Choral counting - record on board and get children to notice the patterns.

When pairing up kids think about personality rather than maths ability.
 Don’t change the pairs all the time, give them some stability.

Finger on the arm as a signal ‘I need more thinking time.’

Revoicing - making what they said more succinct.  Remember to go back to kids
‘Is that what you meant?’

Class Dojo mindset videos - make links to them when kids are struggling.

Independent activities - purpose to these activities

Construction

Pattern blocks

Jigsaws

Threading

Focus or task card to support it.  

Number investigations - eg. have a number and they tell you all they know about that number.  

Maths detective activities for a guided reading book - make up a task card for a book.  

Maths detective box for little ones - make a box of some books with a magnifying glass
and they can find numbers and other maths in the books.

Spot the Difference books.

Simon Says/Boppit game

Memory

Memory match - one group per day, promote to parents too.  

Board games

Ipad games

DMIC PD 26/2/18

We had a PD session on DMIC in our staff meeting on Monday where we practised working on a maths problem collaboratively at different levels.

Key messages from the session were:
- The maths problem needs to be challenging enough that no one child can solve it on their own - they need to work collaboratively.

- The teacher needs to have high expectations of all students.  These can be used to motivate - e.g. 'I'm going to give you a really tricky problem because I know you are capable.' This can empower children.

- The problems need to be engaging.  For example use a cultural context or something that the children are into.

I found it useful to have the facilitator clarify some points about how the maths lesson should be set up and structured.

- The groups should be pre-organised and written into the modelling books.  Year 0-2 children should be in pairs, or if a child is a non-counter, buddied up with two counters.

- The half of the class that is not working with the teacher should be engaged in quiet, meaningful work, but DMIC does not specify exactly what this is.  It could be a problem they have worked on with the teacher the previous day but with the numbers changed.

- The warmup is not a chance to teach the strategy that will be used in the problem but a chance to work on number knowledge etc.  It can be something unrelated to the problem, for example choral counting.

- The teacher should keep a journal with anecdotal notes about how the children approach the problems.  This 'professional noticing' helps teachers to understand where children are at.

- Maths planning should be shared in team meetings.

- Role playing can be used to set up the routine parts of the sessions - for example children can role play speaking in a clear voice to the class (and what happens if they mumble when presenting).

- For juniors, when a group is presenting, the teacher draws what they are saying.

- Connect back to the big idea at the end.

- Connect to the context - if the answer is '435' - '435 what?'

Observing maths in Room 9

I watched Karen S. teaching a maths lesson in her Year 3 class.  I found it valuable to see practical aspects of how she set up the lesson.

Karen had the problem set up in modelling books for the groups to use.  The problem was: "Mrs Schwenke bought 3 groups 15 currant buns from the market.  How many currant buns did Mrs Schwenke buy altogether?

Karen put the children into 3 groups of 4 and got them to explain what was happening in the story.  She used the 'talk moves' language, saying "Can I revoice it for you?"

When the children understood what the problem was about they worked with their groups - Karen chose who was going to be the writer for each group (everyone wanted to write).

When it came to presenting the answers Karen put the children into lines.  When a group was presenting and drawing circles on the modelling book she asked "What do the circles represent?"  I thought this was a good idea, making the connection that the circles represent something from the problem.  Karen was encouraging, saying "Well done for being brave and attempting this," reinforcing positive attitudes towards maths.

After the children had presented their answers Karen made the connection that the problem could be represented as 3 x 15, which was the same as 15+15+15.

Lilianne reminded the children about splitting numbers, that it could be worked out as 3x10 + 3x5, so 30 + 15 = 45.  She reminded them that this is called the distributive law.

Takeaway:  I liked the way that Karen glued the maths problems into modelling books to keep track of them and so that the children could read the problem close up (one of the maths mentors mentioned that this affects their processing of what they read).  I liked the way she set up her groups with everyone sitting in lines and a specific job in the group for each person.  It was good to see the way she used the language from the talk moves and that she encouraged the children for being brave and standing in front of the class, acknowledging that it could be difficult to do this.  

Observation 29/6/17 - Maths

I watched Siale’s maths today in Room 7.  Half the class were doing repeated addition with her and the other half were working on independent problems.

First, Siale revisited the group norms and reminded the children that the norms apply to any group, like a sports team too.  She used humour - “Remember we are family, don’t let the little red hen do all the work” to reinforce this.

The class were doing a repeated addition problem.  “If Anzac had $2, then his nana gave him $2, then his uncle gave him $2, then his mum gave him $2, how much money did he have altogether?

Siale asked questions to clarify:

“What is the problem about?”

“Who is in the story?”

“What did she (Mum) do?”

“How do you know?”

“How many numbers are there?”

“What’s it called?” “Repeated addition.”

Then she said “Ok.  Let’s attack the problem.”

I liked the way she asked questions that drew out the children’s thinking.  

After the children had worked on the problem for a while, Siale rang a bell to signal it was time to stop.  I liked this non-verbal signal - it reminded me that I could use my bell for this.

I also liked her reminder for putting away the pens - “Lid on, pen down, lid on, pen down.”

Two groups presented their answers.  Siale was careful to position them so that they weren’t blocking the board.  After they had explained their answers she brought the rest of the class to the mat and talked to them about repeated addition and how that can be represented as multiplication, the ‘x’ sign meaning ‘groups of.’  She got the children to role play making 6 groups of 2, and 2 groups of 6, showing the reversibility of these factors.  

She then modelled place value in this kind of problem - “If you know that 2 + 2 = 4, you know that 20 + 20 = 40, 200 + 200 = 400 and 2000 + 2000 = 4000.  

Takeaway: From observing this lesson I saw the power of getting children to role play the problem, giving a visual representation.  It was interesting to observe Siale’s careful questioning and this has given me ideas about the way I will launch maths problems in my class.  

Observation 22/2/17 - maths in Room 21

Today I observed Lilianne teaching maths in Room 21 with Year 5s.

They were working on the problem “Team Matai’s classes were using 3579 ipads and Team Manuka’s were using 1756.  How many were they using altogether?”

I liked the way Lilianne got the children to read the problem then flip their papers  over while she clarified parts of the problem.  

Another group was working with Niu in the back room on working out what ⅜ of the number of ipads was.  An important message I noticed Niu giving the children was “You must always give a reason for your answer.”

The first group that explained their answer split the numbers into thousands, hundred, tens and ones and added those.  

Takeaway: I liked the way Lilianne made a link back to the context of the problem at the end, saying “That was a lot of ipads to add up.”  That was a good reminder to me to do the same, so that the problem remains meaningful in its context.  

Observation 8/2/17 - maths in Room 21

Maths in Room 21
Today on my PRT day I observed a maths lesson with Year 5 children, as I have been learning about the 'Bobby Maths' approach.  To start with the teacher, Niu, got the children in pairs to talk about the maths norms - they clarified what some of these meant.  For example, for "Depth is more important than speed" one boy said "Depth means going deep into your brain." Niu also clarified the expectations for the maths programme - that children need to contribute to their groups - "No passengers" and need to ask questions if they don't understand.The problem they were working on was one they had done for homework "If 297 people attend a church and 229 stop attending, how many will be left?"  There were a few variations on this problem and the children were able to select which one they wanted to answer.  The teachers in this classroom had identified subtraction as an area that needed work so were focusing on this. The children got into small groups (4 is the ideal size) and worked on solving the problem.  They had a range of strategies - some split the number into hundreds, tens and ones and subtracted using these, one group used an algorithm, one group used materials, one used a number line...After about 10 minutes the groups got back together and each one had to demonstrate their strategies.  The other groups were encouraged to ask questions if they needed clarification and the teacher asked them to check that they could add their numbers together to check that their equations were correct. The main learning I took away from watching this was that children were discouraged from putting their hands up so that everyone was engaged, not just those who wanted to put their hands up.  I need to check whether this was the policy in all curriculum areas in this class or just in the maths programme.  I noticed that this increased engagement and the idea of 'no passengers.' I will be interested to see how this approach works with my Year 2s.

Takeaway: Encourage children not to put their hands up at maths time - emphasise the idea that anyone can be called on and that everyone needs to be engaging with the problem.

Observation - maths in Room 4 15/2/17

It was interesting today watching a maths lesson with children the same age as my class, after watching Lilianne teaching maths with the older children.  

For Shabnam’s warmup she got the children skip-counting in 2s by getting them to clap one quiet clap then one loud clap.  

She also got them to show her numbers with their hands and was then able to check their understanding quickly.  She got them to make doubles with their hands.  

She then set up the group norms - “How do you work as a team?”  While the children talked about that Shabnam settled the other group, who were working on equations in their books.  

The problem Shabnam was working on with her group was “At church lots of people came.  There were 17 boys and 10 girls.  How many people came to church.”  She connected it to the children’s prior knowledge, asking “Who goes to church?  What do you do at church?”

She then asked “What is the question asking you to do?” One child said “put together” and Shab asked “What are we putting together?” She asked some children to repeat others’ answers and got them to agree/disagree/say they’re not sure with their thumbs.  

I found it really helpful seeing how Shab set the problem up and connected it to the students’ own lives, and her use of the think/pair/share strategy.  

She brought the children back to the mat when some of them were not coping with the problem and asked them “What were you counting?” - linking back to the context of the problem.  She reinforced listening to others “What did Irma just say?” She drew one pair’s explanation on the board - they had drawn each person - then explained there is an easier way to do this - to count on from the bigger number.  They held their heads to practise putting the bigger number in their heads then practised a few examples with this new technique.  

4. demonstrate commitment to ongoing professional learning and development of personal professional practice

i. identify professional learning goals in consultation with colleagues ii. participate responsively in professional learning opportunities within the learning community iii. initiate learning opportunities to advance personal professional knowledge and skills

Maths in Room 21

Today on my PRT day I observed a maths lesson with Year 5 children, as I have been learning about the 'Bobby Maths' approach.  To start with the teacher, Niu, got the children in pairs to talk about the maths norms - they clarified what some of these meant.  For example, for "Depth is more important than speed" one boy said "Depth means going deep into your brain."

Niu also clarified the expectations for the maths programme - that children need to contribute to their groups - "No passengers" and need to ask questions if they don't understand.

The problem they were working on was one they had done for homework "If 297 people attend a church and 229 stop attending, how many will be left?"  There were a few variations on this problem and the children were able to select which one they wanted to answer.  The teachers in this classroom had identified subtraction as an area that needed work so were focusing on this.

The children got into small groups (4 is the ideal size) and worked on solving the problem.  They had a range of strategies - some split the number into hundreds, tens and ones and subtracted using these, one group used an algorithm, one group used materials, one used a number line...

After about 10 minutes the groups got back together and each one had to demonstrate their strategies.  The other groups were encouraged to ask questions if they needed clarification and the teacher asked them to check that they could add their numbers together to check that their equations were correct.

The main learning I took away from watching this was that children were discouraged from putting their hands up so that everyone was engaged, not just those who wanted to put their hands up.  I need to check whether this was the policy in all curriculum areas in this class or just in the maths programme.  I noticed that this increased engagement and the idea of 'no passengers.' I will be interested to see how this approach works with my Year 2s.

PTC 4

4. demonstrate commitment to ongoing professional learning and development of personal professional practice

i. identify professional learning goals in consultation with colleagues ii. participate responsively in professional learning opportunities within the learning community iii. initiate learning opportunities to advance personal professional knowledge and skills

Skittles and fruit loops

We did algebra for our strand maths last week and to make our patterning a bit more hands-on I brought in some skittles and fruit loops.  We practised continuing patterns on pattern cards and making up and recording our own patterns.  

 The student engagement in this activity reminded me of the importance of making lessons hands-on and using different materials to demonstrate ideas.  Having encountered the materials in everyday life made connections between prior experiences.

PTC 8. Demonstrate in practice their knowledge and understanding of how ākonga learn
i. enable ākonga to make connections between their prior experiences and learning and their current learning activities